Equivalent Definitions of A Closed Set
In a topological space, a set is closed if and only if it coincides with its closure. Equivalently, a set is closed if and only if it contains all of its limit points.
This is not to be confused with a closed manifold.
Read more about this topic: Closed Set
Famous quotes containing the words equivalent, definitions, closed and/or set:
“Divorce is the psychological equivalent of a triple coronary bypass.”
—Mary Kay Blakely (20th century)
“The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
—Pamela Patrick Novotny (20th century)
“On a flat road runs the well-trained runner,
He is lean and sinewy with muscular legs,
He is thinly clothed, he leans forward as he runs,
With lightly closed fists and arms partially raised.”
—Walt Whitman (1819–1892)
“This book was written in good faith, reader. It warns you from the outset that in it I have set myself no goal but a domestic and private one.... I am myself the matter of my book.”
—Michel de Montaigne (1533–1592)